U.S. patent application number 09/795955 was filed with the patent office on 2001-10-04 for filter and method and apparatus for manufacturing filters.
Invention is credited to Hunter, Ian, Rhodes, John.
Application Number | 20010026200 09/795955 |
Document ID | / |
Family ID | 26308983 |
Filed Date | 2001-10-04 |
United States Patent
Application |
20010026200 |
Kind Code |
A1 |
Rhodes, John ; et
al. |
October 4, 2001 |
Filter and method and apparatus for manufacturing filters
Abstract
A method of producing filters using lower unloaded Q factor
components than filters with the same performance characteristics
but requiring higher unloaded Q factor components is disclosed. The
method includes the steps of defining a desired filter
characteristic and applying an algorithm which provides a filter
having infinite Q factor elements and having a theoretical
characteristic corresponding to the desired characteristic
transformed to a compensate for the difference between finite Q
factor and infinite Q factor elements.
Inventors: |
Rhodes, John; (Saltair,
GB) ; Hunter, Ian; (Saltair, GB) |
Correspondence
Address: |
MADSON & METCALF
GATEWAY TOWER WEST
SUITE 900
15 WEST SOUTH TEMPLE
SALT LAKE CITY
UT
84101
|
Family ID: |
26308983 |
Appl. No.: |
09/795955 |
Filed: |
February 28, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
09795955 |
Feb 28, 2001 |
|
|
|
09155169 |
Jan 14, 1999 |
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Current U.S.
Class: |
333/167 ;
333/168; 333/175 |
Current CPC
Class: |
H01P 1/20 20130101 |
Class at
Publication: |
333/167 ;
333/168; 333/175 |
International
Class: |
H03H 007/075 |
Foreign Application Data
Date |
Code |
Application Number |
Mar 23, 1996 |
GB |
9606178.3 |
Claims
1. A method of designing a filter, comprising the steps of: (i)
defining a desired filter characteristic; and (ii) applying an
algorithm to the desired filter characteristic to provide a filter
having infinite Q factor elements and having a theoretical
characteristic corresponding to the desired characteristic
transformed to compensate for the difference between~finite Q
factor and infinite Q factor elements.
2. A method of manufacturing a filter, comprising the steps of: (i)
designing a filter according to the method of claim 1; and (ii)
constructing using finite Q factor elements a filter corresponding
to the theoretical filter.
3. A method according to claim 1 or claim 2, in which the algorithm
includes the step of shifting a pole/zero plot of the desired
filter characteristic by a constant amount.
4. A filter manufactured according to the method of any of claims
1-3.
5. Apparatus for use in manufacturing filters, comprising an input
means in which a desired filter characteristic is defined in use,
and means for applying an algorithm to the desired characteristic
to provide a filter having infinite Q factor elements and having a
theoretical characteristic corresponding to the desired
characteristic transformed to compensate for the difference between
infinite Q and finite Q factor elements.
6. Apparatus according to claim 5, in which the algorithm includes
the step of shifting the pole/zero plot of the desired filter
characteristic by a constant amount.
7. A filter manufactured using the apparatus of claim 5 or claim
6.
8. A filter comprising first and second resonators interconnected
by a quadruplet of impedance inverters, a ladder network connected
to the quadruplet of impedance inverters via a series resistor and
comprising a plurality of further resonators, wherein adjacent
further resonators of the ladder network are coupled to each other
by respective impedance inverters.
9. A filter according to claim 8, which is a reflection mode
filter.
10. A filter according to claim 8 or claim 9, which is a microwave
filter.
11. A filter according to any of claims 8-10, which is a bandstop
filter.
12. A filter according to any of claims 8-10, which is a band pass
filter.
13. A method of designing a filter substantially as hereinbefore
described with reference to the accompanying drawings.
14. Apparatus for manufacturing a filter substantially as
hereinbefore described with reference to the accompanying
drawings.
15. A filter substantially as hereinbefore described with reference
to the accompanying drawings.
Description
[0001] The present invention relates to filters and to a method and
apparatus for manufacturing filters, and relates particularly, but
not exclusively, to microwave filters and a method and apparatus
for manufacturing microwave filters.
[0002] Microwave filters are often constructed from networks of
coupled passive resonators, each passive resonator having a finite
unloaded Q factor. In narrow bandwidth applications, the resistive
loss associated with this finite unloaded Q factor can lead to
significant reduction in achievable performance, and in bandpass
applications, designs with a good input and output reflection
coefficient will exhibit significant bandpass loss variation.
[0003] In the narrow band bandstop case the resistive loss
manifests itself as a roll off of insertion loss into the pass
band, and also limits the achievable notch depth. The combination
of these two effects limits the achievable selectivity from a
bandstop filter designed using previously available techniques.
[0004] In an existing bandstop filter, resonators are coupled off
from a main through transmission line with an electrical separation
of an odd number of quarter wavelengths, as shown in FIG. 1. Each
resonator couples loss into the system, giving rise to the problems
outlined above.
[0005] In various applications of microwave filters, such as in
base stations for cellular telecommunications, the above
difficulties are addressed by using components having very high Q
factors, typically up to 40,000. However, this increases the
physical size of the devices involved, whereas it is usually
desirable in such applications to make the devices as compact as
possible.
[0006] Preferred embodiments of the present invention seek to
provide a filter which, although constructed using finite Q
elements, does not suffer from a reduction in selectivity as a
result of resistive losses caused by these finite Q factor
elements.
[0007] Preferred embodiments of the present invention also seek to
achieve a desired filter characteristic using components having
lower unloaded Q factor than in the case of the prior art.
[0008] Preferred embodiments of the present invention also seek to
provide a bandstop/pass filter having a steep transition between
the stop and pass band and using lower value unloaded Q factor
components than in the case of the prior art.
[0009] According to an aspect of the present invention, there is
provided a method of designing a filter, the method comprising
defining a desired filter characteristic, and applying an algorithm
to the desired characteristic to provide a filter having infinite Q
factor elements and having a theoretical characteristic
corresponding to the desired characteristic transformed to
compensate for the difference between finite Q factor and infinite
Q factor elements.
[0010] According to another aspect of the present invention, there
is provided a method of manufacturing a filter, the method
comprising the steps of designing a filter according to a method as
defined above, and constructing using finite Q factor elements a
filter corresponding to the theoretical filter.
[0011] This provides the advantage of a filter design technique
which takes resistive losses of the individual components, such as
inductors and-capacitors, of the filter into account, and therefore
enables a filter having a desired characteristic to be designed
using finite Q value components. This in turn enables a filter
having a particular characteristic to be realised using lower
unloaded Q factor components than in the case of the prior art,
which in turn enables the filter to be constructed more compactly
than in the case of the prior art.
[0012] According to another aspect of the present invention, there
is provided a: apparatus for use in manufacturing filters, the
apparatus comprising an input means in which a desired filter
characteristic is defined in use, and means for applying an
algorithm to the desired characteristic to provide a filter having
infinite Q factor elements and having a theoretical characteristic
corresponding to the desired characteristic transformed to
compensate for the difference between infinite Q and finite Q
factor elements.
[0013] According to a further aspect of the invention, there is
provided a filter manufactured according to a method or using an
apparatus as defined above.
[0014] This has the advantage of enabling the realisation of a
filter having lower Q value components than in the case of the
prior art, which in turn enables the construction of a more compact
filter.
[0015] According to a further aspect of the invention, there is
provided a filter comprising first and second resonators
interconnected by a quadruplet of impedance inverters, a ladder
network connected to the quadruplet of impedance inverters via a
series resistor and comprising a plurality of further resonators,
wherein adjacent further resonators of the ladder network are
coupled to each other by respective impedance inverters.
[0016] In a preferred embodiment, the filter is a reflection mode
filter.
[0017] The filter is preferably a microwave filter.
[0018] A filter may be a bandstop and/or a band pass filter.
[0019] Preferably, the step of applying said algorithm comprises
shifting the pole/zero plot of the desired filter characteristic by
a constant amount.
[0020] A preferred embodiment of the invention will now be
described, by way of example only and not in any limitative sense,
with reference to the accompanying drawings, in which:
[0021] FIG. 1 shows a conventional bandstop filter;
[0022] FIG. 2 shows a reflection mode filter comprising a low loss
circulator connected to an input of a microwave band pass
resonator;
[0023] FIG. 3 shows a lossless low pass ladder network;
[0024] FIG. 4 shows a network comprising a resistive attenuator
followed by a lossless ladder network in which N=3;
[0025] FIG. 5 shows a complete synthesis cycle for a degree 4
network;
[0026] FIG. 6 shows a network corresponding to the network of FIG.
5 modified by the replacement of the first four elements shown in
FIG. 5 by a quadruplet of impedance inverters and two
capacitors;
[0027] FIG. 7 shows a reflection mode band stop microwave
filter;
[0028] FIG. 8 shows the simulated frequency response of the filter
of FIG. 7;
[0029] FIG. 9 shows a general Nth degree circuit for the band stop
reflection mode filter of FIG. 7; and
[0030] FIG. 10 shows the measured frequency response of an actual
filter.
[0031] Referring to FIG. 2, there is shown a resonant circuit with
finite loss which is coupled to one of the ports of a circulator.
The transmission characteristic from ports 1 to 3 is the reflection
coefficient from the network connected at port 2. If the input
coupling to the resonant circuit is adjusted so that the resistive
part of its input impedance is matched to the circulator, then at
resonance all power supplied at port 1 will emerge at port 2 and be
absorbed in the resistive part of the resonator.
[0032] Hence there is no transmission to 3 and the 1-3 transmission
characteristic is that of a resonator with infinite unloaded Q. For
a resonator of centre frequency fo and 3 dB bandwidth B the
unloaded Q is given by 1 Qu = 2 fo B ( 1 )
[0033] For example, if B=250 KHz and fo=1 GHz, then Qu=8000. It can
therefore be seen that the previously considered specification can
be met with much lower Q resonators, with a consequent reduction in
physical size, provided that a design procedure for multi-element
filters is available.
[0034] In order to provide such a design procedure, the magnitude
squared of the input reflection coefficient of a lossless lowpass
prototype filter may be expressed as 2 s 11 ( j ) 2 = F N 2 ( ) 1 +
F N 2 ( )
[0035] Where F.sub.N(.omega.) is the characteristic function for a
Butterworth, Chebychev, Elliptic Function or other prototype
network. This reflection coefficient may readily be synthesised as
a lossless lowpass ladder network which is terminated in a resistor
as shown in FIG. 3. In order to include eventual resonator losses
we can multiply by an arbitrary constant K to yield; 3 s 11 ( j ) 2
= KF N 2 ( ) 1 + F N 2 ( )
[0036] This may now be synthesised as a resistive attenuator
followed by a lossless ladder network which in turn is terminated
in a resistor, as shown in FIG. 4.
[0037] The resultant network now contains dissipative elements.
However, these are not distributed throughout the Nth degree
network but remain concentrated at the input. A network containing
lossy elements is required so that the required response can be
achieved using finite Q resonators.
[0038] In order to achieve this, compensation is made for eventual
resonator loss by shifting the poles and zeros of S.sub.11(p)
towards the j.omega. axis by a constant amount .alpha., i.e. 4 p p
- Thus for s 11 ( p ) = KN ( p ) D ( p ) Then s 11 ( p - ) = KN ( p
- ) D ( p - ) ( 1 )
[0039] The reflection coefficient given in (1) may now be
synthesised as one port impedance function. First the maximum value
of K must be uniquely determined for any specific value of .alpha.,
so that the resultant network is passive and has minimum loss for a
given value of .alpha..
[0040] The specific frequencies .omega..sub.o and values of K are
then determined such that: 5 s 11 ( p - ) 2 = 1 and s 11 ( p - ) 2
= 0
[0041] are simultaneously satisfied with the minimum value of
K.
[0042] Having found the values .omega..sub.o and .alpha. then
formulate 6 s 11 ( p - ) = KN ( p - ) D ( p - ) = N1 ( p ) D1 ( p
)
[0043] The input impedance Zin (p) may now be found from 7 Zin ( p
) = D 1 ( p ) + N 1 ( p ) D 1 ( p ) - N 1 ( p )
[0044] Zin has a transmission zero at .omega..sub.o and thus cannot
be synthesised as a ladder network.
[0045] However any positive real function may be synthesised using
Brunes' Procedure as set out in O Brune. "Synthesis of a Finite
Two-Terminal Network whose Driving Point Impedance is a Prescribed
Function of Frequency". Journal of Maths and Physics, Vol X no 3,
1931, p 191. 8 Given Yin ( p ) = 1 Zin ( p ) and evaluating Yin at
p = j o it is
[0046] found that this is a pure susceptance. This is a consequence
of the network being purely reflective at that frequency. This
susceptance will be negative i.e.
Yin (j.omega.o)=-jB
[0047] Extracting a shunt negative capacitor of value -C.sub.1 from
Yin provides
Y.sub.1(p)=Yin(p)+C.sub.1p
[0048] Observing that Y.sub.1 is one degree higher in p than Yin
then since Yin (j.omega..sub.o) was purely imaginary, Y.sub.1 must
be equal to zero at this frequency. Consequently Y.sub.1 (p) must
have a quadratic factor at p=.+-.j.omega..sub.o. 9 Y 1 ( p ) = ( p
2 + o 2 ) N ( p ) P ( p )
[0049] Inverting Y.sub.1(p) to form Z.sub.1(p) a series branch
composed of a parallel tuned circuit can be extracted, ie 10 Z 1 (
p ) = D ( p ) ( p 2 + o 2 ) N ( p ) = Ap p 2 + o 2 = Z 2 ( p )
[0050] A is the residue of Z.sub.1(p) at p=j.omega..sub.o.
Inverting Z.sub.2(p) to obtain Y.sub.2(p) then a shunt capacitor
may be extracted from Y.sub.2(p) as follows: 11 C 3 = Y 2 ( p ) p p
= .infin. and Y 3 ( p ) = Y 2 ( p ) - C 3 p Forming Z 4 ( p ) + 1 Y
3 ( p ) .
[0051] A series resistor equal in value to the minimum real part of
Z.sub.4 (p) must now be extracted. This may be evaluated from the
minimum value of the even part of Z.sub.4(p).
Thus Z.sub.5(p)=Z.sub.4(p) -R
where R=min Ev(Z.sub.4(p))
[0052] In most cases the minimum value of Z.sub.4(p) will occur at
.omega.=.infin. and the remaining network may be synthesised as a
lossy ladder network.
[0053] The complete synthesis cycle is shown for a degree 4 network
in FIG. 5.
[0054] It is important to note that the network shown in FIG. 5 is
not immediately suitable for realisation using microwave
resonators. However, it may readily be transformed into the network
of FIG. 6 which consists entirely of inverters, capacitors and
resistors.
[0055] The capacitors shown in FIG. 6 are initially lossless but
are transformed into finite Q elements by the final simple
modification.
p.fwdarw.p+a
[0056] The resultant lowpass prototype network may then be
converted into a bandpass network by applying the appropriate
transformation for any particular type of resonator.
EXAMPLE
[0057] The procedure outlined has been applied successfully to the
design of a bandstop filter with specification as outlined
above.
[0058] A fourth degree Elliptic Function Filter was synthesised.
The choice of .alpha. was 0.093 corresponding to approximately 6 dB
out of band loss. The resultant network is shown in FIG. 7. The
simulated response of this network is shown in FIG. 8, from which
it can be seen that the response achieves the desired
specification. This actual filter has been constructed using
coaxial resonators. The measured performance characteristics are
shown in FIG. 10 and are in excellent agreement with theory.
[0059] It will be appreciated by persons skilled in the art that
the above embodiment has been described by way of example only, and
not in any limited sense, and that various alterations and
modifications are possible without departure from the scope of the
invention as defined by the appended claims.
* * * * *